Three riflemen A, B, and C take turns shooting at a target. The first rifleman to hit the target gets 2002 dollars. A shoots first, B second, and C third, after which the cycle repeats again with A, until one of the riflemen hits the target. Each hits the target with probability 0.5. What is rifleman A's expected winnings in dollars?
According to me, the events are dependent on each other. So, if A hits the target then B and C do not have a chance to get the money. It is the same logic for B and C. We do not know how many times the cycle is repeated until someone wins. So for A to hit the target in the n-th cycle the probability of getting 2002 dollars is (1/2)^n. The three of them have equal probability of getting the money or not. The thing that bothers me is that we do not how many times each of them tries to hit the target until he wins. Does it have anything to do with the answer? Or independently of the number of cycles we can find it?